7.1a Mean

7.1a Mean
1. The mean of the data is an average value obtained by using the formula:
Mean= Total data values Number of data
(A) Ungrouped Data


Example 1
(a) Find the mean for the set of data 2, 4, 7, 10, 13, 16 and 18.

(b) A value of x is added into the above set of data, the mean for
      this new data is 9.5. Determine the value of x.

Solution:
(a)
x ¯ = 2+4+7+10+13+16+18 7 x ¯ = 70 7 =10
(b)
New mean =9.5 70+x 8 =9.5 70+x=76 x=6

(B) Grouped Data (Without Class Interval)

Example 2
The frequency table shows the marks obtained by 40 students in a Biology test.

Marks
50
55
60
65
70
Number of students
6
8
15
10
1

Find the mean marks.
Solution: 
Mean marks,  x ¯ x ¯ = ( 50 )( 6 )+( 55 )( 8 )+( 60 )( 15 )+( 65 )( 10 )+( 70 )( 1 ) 6+8+15+10+1 x ¯ = 2360 40 =59

(C) Grouped Data (With Class Interval)



Example 3
The grouped frequency distribution was obtained from 100 students regarding the scores in their test shown as below.

Scores
Frequency
5 – 9
4
10 – 14
10
15 – 19
19
20 – 24
26
25 – 29
21
30 – 34
12
35 – 39
8
Find the mean scores.

Solution:

Scores
Frequency f
Midpoint x
fx
5 – 9
4
7
28
10 – 14
10
12
120
15 – 19
19
17
323
20 – 24
26
22
572
25 – 29
21
27
567
30 – 34
12
32
384
35 – 39
8
37
296
Total

100
2290
Mid-point= 5+9 2 =7 Mean scores,  x ¯ = fx f = 2290 100 =22.9